enVision Mathematics Topics 1-5
1st Grade; August – November (13 weeks); 1st/2nd Trimester
Embedded Files
Topic Title(s):
Understand Addition and Subtraction (Topic 1)
Fluently Add and Subtract Within 10 (Topic 2)
Addition Facts to 20: Use Strategies (Topic 3)
Subtraction Facts to 20: Use Strategies (Topic 4)
Work with Addition and Subtraction Equations (Topic 5)
Prepared Graduates:
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP7. Look for and make use of structure.
Standard(s):
2. Algebra and Functions
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
1.OA.A. Operations & Algebraic Thinking: Represent and solve problems involving addition and subtraction.
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (see Appendix: Table 1) (CCSS: 1.OA.A.1)
Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (CCSS: 1.OA.A.2)
1.OA.B. Operations & Algebraic Thinking: Understand and apply properties of operations and the relationship between addition and subtraction.
Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (CCSS: 1.OA.B.3)
Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. (CCSS: 1.OA.B.4)
1.OA.C. Operations & Algebraic Thinking: Add and subtract within 20.
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). (CCSS: 1.OA.C.5)
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).* (CCSS: 1.OA.C.6)
1.OA.D. Operations & Algebraic Thinking: Work with addition and subtraction equations.
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. (CCSS: 1.OA.D.7)
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = __ – 3, 6 + 6 = __. (CCSS: 1.OA.D.8)
Make sense of problems by relating objects, drawings, and equations. (MP1)
Use cubes, number racks, ten frames and other models to represent addition and subtraction situations in real-world contexts. (MP4)
Make sense of addition and subtraction by applying properties of operations and working with different problem types (see Appendix, Table 1). (MP1)
Use properties of operations to recognize equivalent forms of equations. (MP7)
Use multiple strategies to think about problems and see how the quantities involved support the use of some strategies over others. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
Make use of the structure of numbers when making tens or when creating equivalent but easier or known sums. (MP7)
Make sense of quantities and their relationships in problem situations. (MP2)
Question assumptions about the meaning of the equals sign and construct viable arguments. (MP3)
Inquiry Questions
How can you use cubes to help you compare two numbers?
(Given a representation of a value less than ten) How many more do you need to make ten?
How could you explain why 3 + 8 and 8 + 3 both equal 11?
How can you use the number line to show how you might use adding OR subtracting to solve the same problem?
Which would you prefer when adding 4 + 7: starting with 7 and counting up 4 or starting with 4 and counting up 7? Why?
Why does knowing doubles like 4 + 4 or 5 + 5 help when adding 4 + 5?
How does counting on to add and subtract within 20 make it easier to use fingers even though we have only 10 fingers?
What does it mean for two sides of an equation to be “equal”? How can 2 + 3 “equal” 5?
(Given 4 = 4) If you add 2 more to the 4 on the right, how many do you need to add on the left to make a true statement? How would you write that as an equation?
Coherence Connections
This expectation represents major work of the grade.
In kindergarten, students add and subtract within 10 by using objects or drawings to represent problems.
In previous grades, students model and describe addition as putting together and adding to, and subtraction as taking apart and taking from, using objects or drawings.
In kindergarten, students understand the relationship between numbers and quantities and connect counting to cardinality.
In kindergarten, students represent addition and subtraction with equations without needing to understand the meaning of the equal sign.
In Grade 1, this expectation connects with comparing, adding, and subtracting numbers, including measurement and data activities.
In Grade 1, this expectation connects with representing and solving problems involving addition and subtraction and with adding and subtracting within 20.
In Grade 1, this expectation connects with place value understanding, properties of addition and subtraction, the relationship between addition and subtraction, and with representing and solving problems involving addition and subtraction.
In Grade 1, this expectation connects with representing and solving problems involving addition and subtraction.
In Grade 2, students represent and solve real-world problems involving addition and subtraction within 100, with fluency expected within 20.
In future grades, students use place value understanding and properties of operations to add and subtract within larger number ranges, then to perform multi-digit arithmetic. Later, students use these concepts to build fractions from unit fractions, and to apply and extend their understandings of arithmetic to algebraic expressions.
In Grade 2, students fluently add and subtract within 20 using mental strategies and know from memory all sums of two one-digit numbers.
In Grade 2, students work with equal groups of objects to gain foundations for multiplication. In Grade 4, students build fractions from unit fractions and apply addition and subtraction to concepts of angle and angle measurement.
Academic Vocabulary & Language Expectations:
Add, plus, sum, parts, whole, equation, subtract, minus, difference, more, compare, fewer, addend, number line, doubles fact, near doubles fact, count back, open number line, doubles-plus facts, make 10, related facts, fact family
Assessments:
Topics 1-2 Assessment (PDF), Topic 3 Assessment (PDF), Topic 4 Assessment (PDF), Topic 5 Assessment (PDF)
Instructional Resources & Notes:
enVision Mathematics Topics 1-5
Additional enVision Mathematics Resources
Let's Investigate! Bird Watching (TE) (supports Lessons 1-7, 1-8)
Let's Investigate! Scaredy Cats Game (TE) (supports Lessons 2-7, 2-8)
Let's Investigate! Big Celebrations (TE) (supports Lessons 3-6, 3-7)
Let's Investigate! Sneaky Squirrels (TE) (supports Lessons 4-4, 4-5)
Let's Investigate! True or False (TE) (supports Lessons 5-3, 5-4)
3-Act Math Recording Sheets (Topic 1, Topic 3, Topic 5)
Supplemental Lesson Resources: Topic 1, Topic 2, Topic 3, Topic 4, Topic 5
Additional Math Games: Addition & Subtraction Within 20 (additional materials and preparation may be required)
Notes:
Topic 1 should not be assessed for mastery; the various word problem forms are used throughout Topics 1-5 for addition and subtraction within 20. Topics 1-2 should be assessed together.
*Students do not need to show mastery of all the strategies presented in Topics 3-4; rather, students should have exposure to a wide range of computational strategies to build number sense, using strategies that make sense to them when solving problems in multiple ways.
Students are expected to use the number line to add and subtract within 100 in 2nd Grade.
It is recommended to move the 3-Act Math Task in Topic 5 (Weighted Down) to the end of the Topic.
Topic 1 Readiness Resources:
Prior to Topic 1, spend up to ten days reviewing assumed prior knowledge and foundational skills with writing numbers, counting, and comparing quantities from Kindergarten. Activities and tasks may include:
Kindergarten Counting and Cardinality Routines (choose as appropriate): "Domino Partners," "Five and More," "How Many Are Hiding (with 10)?," "Partner Flash," "Rows and Columns"
1st Grade Number and Operations Routines (choose as appropriate): "How Many Days?," "How Many Ways," "In and Out," "More or Less Than 120," "Mystery Number," "Number of the Day," "Ooh! and Ahh!"
Illustrative Mathematics Tasks (choose as appropriate): Number of the Day, Choral Counting II
Grade 1 Readiness Pages (choose as appropriate): Writing Numbers 0 to 4 (R1), Writing Numbers 5 to 9 (R2), Counting and Writing to 9 (R3), Comparing Numbers Through 5 (R4), Comparing Numbers Through 10 (R5), Making Numbers 6 to 9 (R6), Finding Missing Parts of Numbers 6 to 9 (R7), Shapes (R8) (these pages are in the student consumable workbook before Topic 1)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention Topics 1-2: Solve Word Problems with Totals to 10, Count On to Add, Number Pairs for Sums to 10, Doubles Addition Facts, Find Missing Addends, Count On to Subtract, Addition and Subtraction Facts
Tier 1 Intervention Topic 3: Make a Ten to Add Within 20, Totals Greater than Ten
Tier 1 Intervention Topic 4: Subtraction Within 20
Tier 1 Intervention Topic 5: Solve Word Problems with Totals to 20
Coherence Map/Concept Progressions: 1.OA.A.1, 1.OA.B.3, 1.OA.C.6, 1.OA.D.8
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